Abstract: In the case of elastic and plastic contact problem with friction, since the friction law on the contact boundary are expressed by inequalities, the variational formulation of the constraints leads to variational inequalities, instead of variational equalities. The research on the elasto-plastic contact problem with friction and finite displacement is done. The generalized variational principle of elasto-plastic contact problem with friction and finite displacement is derived by use of Lagrange multiplier method. The energy functional of variational inequalities problem is obtained by use of Lagrange multiplier method. It provides a numerical base for these kinds of problems.

Key words: Contact problem, Elasto-plastic theory, Finite displacement, Generalized variational principles, Variational inequalities